<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2015-04-10</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001289236</issuerCik>
        <issuerName>BioMed Realty Trust Inc</issuerName>
        <issuerTradingSymbol>BMR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001639638</rptOwnerCik>
            <rptOwnerName>Berens James R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>17190 BERNARDO CENTER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN DIEGO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>92128</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President, Wexford</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>34828</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Limited Partnership Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>272491</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Waterford Equities, LLC</value>
                </natureOfOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Limited Partnership Units in BioMed Realty, L.P. 34,246 Limited Partnership Units are eligible to vest subject to the satisfaction of certain performance conditions and other conditions every six months through December 1, 2017.  238,245 Limited Partnership Units are subject to time-based restrictions which lapse on May 31, 2017.   After the satisfaction of applicable conditions, Limited Partnership Units are redeemable for cash based upon the fair market value of an equivalent number of shares of common stock of BioMed Realty Trust, Inc. (the &quot;Company&quot;), or, at the election of the Company, shares of the Company's common stock on a 1-for-1 basis.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Jonathan P. Klassen, Attorney-In-Fact</signatureName>
        <signatureDate>2015-04-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
